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Solve for real x: |x² + 3x + 2| + x + 1 = 0.

1. x = -1 and x = -3
2. x = -1 only
3. x = -2 and x = -3
4. No real solution

Correct answer: x = -1 and x = -3

Solution

Removing the absolute value requires casework on the sign of (x+1)(x+2). Each case gives a quadratic whose roots must be checked against the case's interval.

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